Equal mass of oxygen and helium gases are mixed in a container at 27°C Fraction of total pressure exerted by helium gas is

Options

A. `1/8`
B. `8/9`
C. `1/9`
D. `3/4`

Answer

To solve the problem of finding the fraction of total pressure exerted by helium gas when equal masses of oxygen and helium gases are mixed at 27°C, we can follow these steps:

### Step 1: Define the Equal Mass
Let the equal mass of both gases be \( W \) grams.

### Step 2: Calculate the Number of Moles of Helium
The molar mass of helium (He) is 4 g/mol. Therefore, the number of moles of helium can be calculated using the formula:
\[ n_{He} = \frac{W}{\text{Molar mass of He}} = \frac{W}{4} \]

### Step 3: Calculate the Number of Moles of Oxygen
The molar mass of oxygen (O₂) is 32 g/mol. Therefore, the number of moles of oxygen can be calculated as:
\[ n_{O_2} = \frac{W}{\text{Molar mass of O}_2} = \frac{W}{32} \]

### Step 4: Calculate the Total Number of Moles
The total number of moles in the mixture is the sum of the moles of helium and oxygen:
\[ n_{total} = n_{He} + n_{O_2} = \frac{W}{4} + \frac{W}{32} \]

### Step 5: Find a Common Denominator
To add the fractions, we need a common denominator. The least common multiple of 4 and 32 is 32:
\[ n_{total} = \frac{8W}{32} + \frac{W}{32} = \frac{9W}{32} \]

### Step 6: Calculate the Mole Fraction of Helium
The mole fraction of helium (\( X_{He} \)) is given by the formula:
\[ X_{He} = \frac{n_{He}}{n_{total}} = \frac{\frac{W}{4}}{\frac{9W}{32}} \]
Simplifying this:
\[ X_{He} = \frac{W}{4} \times \frac{32}{9W} = \frac{32}{36} = \frac{8}{9} \]

### Step 7: Determine the Fraction of Total Pressure Exerted by Helium
According to Dalton's Law of Partial Pressures, the fraction of total pressure exerted by helium gas is equal to its mole fraction:
\[ \text{Fraction of total pressure by He} = X_{He} = \frac{8}{9} \]

### Conclusion
Thus, the fraction of total pressure exerted by helium gas is \( \frac{8}{9} \).